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Search: id:A123964
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| A123964 |
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A triangular sequence from the omega(5) Jacobian Elliptic Modular equation. |
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+0
1
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| 0, -1, 0, -64, -3, 4080, -729, -128, 29515, 236160, -4096, -1215, 123168, 986873, 4194240, -15625, -6144, 373899, 3004544, 12770391, 39062400, -46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560, -117649, -62208, 1989555, 16131200, 68598447, 209838336, 522579107, 1129900800
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Normally these functions are taken as implicit polynomials in two variables set equal to zero. Row Sum: Table[Sum[t[n, m], {n, 0, m}], {m, 0, 10}] {0, -1, 4013, 264818, 5298970, 55189465, 379059799, 1948857588, 8093819508, 28530904515, 88314392705}
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REFERENCES
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Eric Weisstein's World of Mathematics, "Modular Equation." http://mathworld.wolfram.com/ModularEquation.html
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FORMULA
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t(n,m) =n^6 - m^6 + 5*n^2*m^2*(n^2 - m^2) + 4*n*m*(n^4*m^4 - 1)
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EXAMPLE
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Triangular sequence:
{0},
{-1, 0},
{-64, -3, 4080},
{-729, -128, 29515, 236160},
{-4096, -1215,123168, 986873, 4194240},
{-15625, -6144, 373899, 3004544, 12770391, 39062400},
{-46656, -21875, 925648, 7468533, 31750240, 97119349, 241864560}
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MATHEMATICA
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t[n_, m_] = n^6 - m^6 + 5*n^2*m^2*(n^2 - m^2) + 4*n*m*(n^4*m^4 - 1); a = Table[Table[t[n, m], {n, 0, m}], {m, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A058963 A066608 A085339 this_sequence A065790 A147792 A066539
Adjacent sequences: A123961 A123962 A123963 this_sequence A123965 A123966 A123967
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KEYWORD
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uned,probation,sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 28 2006
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